Timeline for One more question about PBW

6 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Nov 28, 2012 at 18:20	history	edited	DamienC	CC BY-SA 3.0	added 14 characters in body
Nov 28, 2012 at 15:52	answer	added	Jim Humphreys		timeline score: 5
Nov 28, 2012 at 7:52	comment	added	DamienC		I know that PBW holds whenever $k\supset\mathbb{Q}$. About my EDIT, this was just a dummy suggestion for a strategy. I was thinking about something like: if $L\to U(L)$ is injective and if PBW holds for $L\otimes_k\mathbb{K}$ (for some $\mathbb{K}$) then PBW holds for $L$
Nov 27, 2012 at 23:18	comment	added	Theo Johnson-Freyd		How does $L \hookrightarrow U(L)$ reduce to the $k\supseteq \mathbb Q$ case? If $k$ is any field, then all Lie algebras over it have the PBW property. Actually, come to think of it, I think that Lie algebras always have the PBW property when $k \supseteq \mathbb Q$ — my memory is that this is proved in, for example, the article by Deligne and Morgan in QFT and Strings, but flipping through I can't find it. The idea is to prove that the canonical symmetrization map (which requires dividing by all $n!$s) is a filtered isomorphism $S(L) \to U(L)$ covering the canonical map $S(L)\to gr(U(L))$.
Nov 27, 2012 at 21:03	history	asked	DamienC	CC BY-SA 3.0